There exists a uniform magnetic field perpendicular to the plane of the figure in cylindrical region of radius a. The magnetic field is increasing at a constant rate α Ts − 1 . A particle having charg

Question

There exists a uniform magnetic field perpendicular to the plane of the figure in cylindrical region of radius a. The magnetic field is increasing at a constant rate $α Ts^{- 1}$ . A particle having charge q is at a point $P$ outside the field region. The particle is slowly moved to infinity, work done by the external agent on the particle if, the particle is moved in a direction perpendicular to $OP$ along $PQ$ is $\frac{π qa ^{2} α}{n}$ . Find n.

TestHub · Accepted Answer

Induced field at distance r: E ⋅ 2 π r = π a 2 α ⇒ E = 2 r a 2 α ​ With x = d tan θ : d W = 2 q a 2 α ​ d θ W = 2 q a 2 α ​ ∫ 0 π /2 ​ d θ = 4 π q a 2 α ​ ⇒ n = 4

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